On Solving Nearly Incompressible 2D Problems Using an Adaptive Refinement Procedure

Communications In Numerical Methods In Engineering, Wiley, Vol 14, pp.409-418, 1998

MESHING
RESEARCH
CORNER

C. K. Lee
Department of Civil and Structural Engineering, The University of Hong Kong, Hong Kong

R. E. Hobbs
Department of Civil Engineering. Imperial College of Science, Technology and Medicine, London, U.K.

Abstract
A numerical study is carried out employing some selected 2D elements and an automatic adaptive refinement procedure for the solution of a problem involving a nearly incompressible material. For a material with Poisson's ratio close to 0.5, it is found that both hybrid elements and high-order Lagrangian triangles can be used to provide a reliable solution. Furthermore, the rate of convergence of the elements is not affected by the high value of Poisson's ratio, and a near-optimal convergence rate is achieved in all the numerical tests run.